Device and a method for the generation of coherent x-ray radiation

ABSTRACT

A device ( 10 ) for producing high frequency radiation using a source of elliptically polarized radiation is disclosed based on: irradiating a frequency multiplication medium having a screw axis ( 16 ) symmetry of approximate Nth order symmetry, oriented so that said elliptically polarized radiation propagates in parallel to the screw axis ( 16 ). Also, a method for producing high frequency radiation is disclosed based on irradiating a frequency multiplication medium having a screw axis ( 16 ) of approximate Nth order symmetry with elliptically polarized radiation so that the elliptically polarized radiation propagates in parallel to the screw axis ( 16 ). Furthermore, a method of producing a beam of high frequency radiation composed of only a limited number of wavelengths is disclosed whereby the intensity of a beam ( 22 ) interacting with a frequency multiplication medium is selected so that only a limited number of wavelengths is emitted.

FIELD AND BACKGROUND OF THE INVENTION

[0001] The present invention relates to the generation of high frequency coherent electromagnetic radiation such as soft x-rays and, more particularly, to a device and method for producing a beam of this radiation.

[0002] The development of masers and lasers circa 1960 stimulated speculation about the possibility to develop devices that generate coherent electromagnetic radiation with much shorter wavelengths, for example, of soft x-ray wavelengths between about 1 nm and about 10 nm. Such devices could be used in applications including holographic imagine of biological structures, plasma diagnostics and the generation of intense plasmas. More recent advances in other fields have suggested other applications of coherent soft x-rays. For example, a source of coherent x-rays for CT scanning could be operated at a much lower power level than the sources of incoherent x-rays now in use, reducing the exposure of the subjects to ionizing radiation. Another application is in the fabrication of microdevices. The design rule of devices such as integrated circuits is now limited to a lower bound of about 0.1 microns by several factors, not least of which is that the shortest wavelength radiation that can be used for photolithography is ultraviolet radiation. A coherent source of soft x-rays would help make even shorter design rules feasible. Similarly, a coherent source of soft x-rays would enable much denser storage of information in media such as compact disks. A sufficiently intense coherent beam of soft x-rays can be used as an industrial cutting tool.

[0003] Lasers have been used to produce soft x-rays. The first soft x-ray laser was developed at Lawrence Livermore National Laboratory in 1984. This device, which was described in general terms by Dennis Matthews and Mordecai Rosen in the December 1988 issue of Scientific American, uses the Nova laser to create a plasma including high-Z ions and to create a population inversion among those ions by collisional excitation. The laser medium in such a device is inherently transient. Essentially, the mere process of creating the laser medium, by evaporating a metal foil to produce plasma, also destroys the laser medium. The use of the Nova laser, originally developed for controlled fusion research, to create the lacer medium also meant that the device was a large, expensive research tool unsuitable for practical applications. More compact soft x-ray lasers have been developed in recent years, but like their giant ancestor at LLNL, they all rely on inherently self-destructive mechanisms to create a population inversion in a highly ionized plasma.

[0004] Two non-self-destructive strategies for the generation of coherent soft x-rays have been explored. The first is the imposition of spatial periodicity on the trajectories of high-energy electrons in free-electron lasers. This requires the use of a massive high-energy accelerator to create the high-energy electrons.

[0005] The second non-self-destructive strategy for the generation of coherent soft x-rays is the use of frequency multiplication media to create higher harmonics of coherent light. This strategy has led to the development of devices that produces high frequency coherent electromagnetic beams from low frequency coherent electromagnetic beams produced by conventional lasers. A review of the strategy may be found in L'Huiller et al., “High-order harmonics: a coherent source in the XUV range”, Journal of Nonlinear Optical Physics and Materials, July 1995, Vol. 4 No. 3, pp. 647-665, which is incorporated by reference for all purposes as if fully set forth herein.

[0006] Using helium atoms as the frequency multiplication medium, Chang et al. in Phys. Rev. Lett. 79, pp. 2967-2970 (1997) have reported the generation of beams with down to 2.7 nm wavelengths while Schnürer et al. in Phys. Rev. Lett. 80, pp. 3236-3239 (1998) have reported the generation of beams with wavelengths down to shorter than 2.5 nm.

[0007] WO 99/33084, which is incorporated by reference for all purposes as if fully set forth herein, discloses a device where a substantially circularly polarized beam of coherent light is directed at a frequency multiplication medium. The frequency multiplication medium of WO 99/33084 is made up of a material, having constituents, the constituents having an approximate Nth order rotational symmetry axis, oriented so that the Nth order axes of the constituents are substantially parallel to the incident beam. The interaction of the beam and the constituents produces selected higher frequency harmonics of the frequency of the incident beam. If the Nth order rotational symmetry axis is exact, the harmonic frequencies produced are integral multiples of the frequency of the harmonic beam, given by Ω=Nk±1, where k is a positive integer. If the Nth order rotational axis symmetry is only approximate, the harmonics are centered around these multiples. “Approximate Nth order rotational symmetry axis” means that the geometry of the constituents of the frequency multiplication mediau is close enough to having an exact Nth order rotational symmetry axis for the interaction of the frequency multiplication medium with the incident beam to lead to frequency multiplication in accordance with the approximate selection rules. Depending on N and on the frequency of the incident beam, the harmonics produced are up into the soft x-ray band. Suitable medium constituents include molecules with a dipole and C₅ symmetry (such as C₅H₅Tl gas) circular rings of nanoparticles and nanotubes.

[0008] The methods and devices known in the art are insufficient because ordinarily N is not very large, generally N=2 for atoms in monochromatic linearly polarized fields, leading to the emission of many harmonics and thus a broad mixture of wavelengths. For example, N. Sarukura et al. reported in Phys. Rev. A Vol 43 pp. 1669-1672 (1991) the generation of 9^(th) to 23^(rd) order harmonics of light from a KrF laser when using helium as a frequency multiplication medium. Preston et al in Phys. Rev. A Vol. 53 pp. R31-R34 (1996) reported obtaining harmonics up to the 35^(th) using helium as a frequency multiplication medium.

[0009] As is clear to one skilled in the art, for most applications it is preferred that the distribution of wavelengths in the produced beam be as limited as possible.

[0010] There is thus a widely recognized need for, and it would be highly advantageous to have, a compact, portable, reusable source of coherent x-rays with a limited wavelength distribution.

SUMMARY OF THE INVENTION

[0011] According to the present invention there is provided a device for producing high frequency radiation, including: a) a source of elliptically polarized radiation; and b) a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2, and wherein the constituent is oriented so that the radiation propagates substantially parallel to the screw axis.

[0012] According to the present invention there is also provided a method of producing high frequency radiation, including the steps of: a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2; and b) directing elliptically polarized radiation at an angle to the screw axis so that the elliptically polarized radiation propagates substantially parallel to the screw axis

[0013] According to the present invention there is provided a device for producing high frequency radiation, including: a) a source of elliptically polarized radiation; and b) a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2 and also including an axis of approximate C_(n) symmetry, wherein n is at least 3, and wherein the constituent is oriented so that the radiation propagates substantially parallel to the screw axis.

[0014] According to the present invention there is also provided a method of producing high frequency radiation, including the steps of: a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2 and also including an axis of approximate C_(n) symmetry, wherein n is at least 3; and b) directing elliptically polarized radiation at an angle to the screw axis so that the elliptically polarized radiation propagates substantially parallel to the screw axis.

[0015] According to the present invention there is also provided a method of producing a beam of high frequency radiation composed of a limited number of wavelengths by: a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2; and b) directing elliptically polarized radiation at an angle to the axis such that the elliptically polarized radiation propagates substantially parallel to the screw axis. The intensity of the radiation is chosen relative to the frequency of the radiation, the magnitude of N and the geometry of the constituent so that only the desired number of harmonics is produced.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein:

[0017]FIG. 1 illustrates the classification of carbon, boron-nitride, tungsten disulfide, or molybdenum disulfide nanotubes according to the pair of indices (n, m);

[0018]FIG. 2 is a schematic illustration of a first embodiment of the device of the present invention based on nanotubes as a constituent of a frequency multiplication medium; and

[0019]FIG. 3 is a schematic illustration of a second embodiment of the device of the present invention based on nanotubes as a constituent of a frequency multiplication medium where the incident beam is non-nonnal.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] The present invention is of a device and method for the production of coherent circularly polarized light. Specifically, the present invention is used to produce coherent soft x-rays. The principles and operation of the device and the method of the present invention may be better understood with reference to the drawings and the accompanying description.

[0021] According to the method of the present invention, selected higher harmonics of a beam of elliptically polarized electromagnetic radiation are generated by the interaction of the beam with a constituent of a frequency multiplication medium having a screw axis of approximate Nth order symmetry. The interaction causes selected higher frequency harmonics of the incident beam to be emitted from the medium. The selection rule for high harmonic generation is L=pN±1, where L is a generated harmonic, p a positive integer and N the order of the screw axis. Generated are pairs of harmonics. The theoretical background of how this interaction generates a beam of selected higher harmonics of the incident beam is described in the Appendix and in Alon et al., “High Harmonic Generation of Soft X-Rays by Carbon Nanotubes”. Phys. Rev. Lett., Vol. 85 pp. 5218-5221 (11 Dec. 2000).

[0022] According to the Appendix and in Alon et al., conditions for selective high harmonic generation include: the screw axis of the constituent of the frequency multiplication medium having an Nth order, the incident beam being circularly polarized and the incident beam propagating in parallel to the screw axis. As can be experimentally proven by one skilled in the art, any of these three conditions can be relaxed to a certain extend without substantially effecting the selectivity of high harmonic generation. Thus, for practical purposes, the screw axis of the constituent of a used frequency multiplication medium has an approximate Nth order, the incident beam may be elliptically polarized, and the beam must propagate only substantially parallel to screw axis.

[0023] A most basic embodiment of a device of the present invention consists of a beam of coherent elliptically polarized radiation directed at a frequency multiplication medium with a constituent having a screw axis symmetry of approximate Nth order, where the beam propagates substantially parallel to the screw axis.

[0024] Nanotubes are a preferred class of materials for implementing a device of the present invention. Nanotubes are cylindrical molecules, typically composed of carbon, although nanotubes made of other compositions such as boron-nitride, tungsten disulfide or molybdenum disulfide are also known. For the purposes of the present discussion, the case of single walled pure carbon nanotubes will be considered as non-limiting example.

[0025] Single walled carbon nanotubes can be viewed as graphite sheets rolled up into cylindrical structures. The infinite order of translational symmetries of the graphite lattice transforms into various finite order symmetries once the graphite sheet is rolled-up to make a nanotube. The order and character of the resulting symmetries depend on the way the graphite sheet boundaries are connected with each other to form the nanotube cylinder. In FIG. 1, the accepted classification of carbon nanotubes, according to the pair of indices (n,m), is illustrated. A (n,m)-carbon nanotube is formed by rolling the graphite sheet along the chiral vector C_(h)=n{overscore (a)}₁+m{overscore (a)}₂, such that its origin O and its end point O′ coincide in the nanotube. If the graphite sheet is rolled along the n{overscore (a)}₁ direction then a zigzag nanotube classified by the pair of indices (n,0) is formed. If the graphite sheet is rolled along the n({overscore (a)}₁+{overscore (a)}₂) direction then all armchair nanotube classified by the pair of indices (n,n) is formed. In all other cases, that is whenever 0<m<n, a chiral nanotube is formed.

[0026] For example, when a (12,6)-carbon nanotube having a screw axis with the order N=84 is irradiated in accordance with the method of the present invention with a beam with a wavelength of 248 nm and an intensity in the range of about 6-9×10¹³ Watt/cm² (such as produced by a KrF laser) the emitted harmonics produced have a wavelength of 2.99 and 2.92 nm corresponding to the 83d and 85th harmonics. The two following symmetry-allowed harmonics, the 167th and 169th are emitted at an extremely low intensity if at all, as described in the Appendix and in Alon et al.

[0027] From this example, an added advantage of the present invention over the prior art is seen. As discussed above, harmonic generation methods known in the prior art produces a wide range of wavelengths in the emitted beam. The harmonics appear as a plurality of frequencies. As is well known to one skilled in the art and described in the Appendix and in Alon et al., there exists a cutoff frequency above which the intensity of the generated harmonics falls-off exponentially. The cutoff frequency when a nanotube is used in the frequency multiplication medium is determined by the diameter of the nanotube as well as the frequency and the strength of the electrical field of the incident radiation. Some molecules, such as chiral nanotubes, have screw axes with very high orders. A specific such molecule can be chosen for use as constituent in a frequency multiplication medium according to the present invention along with an incident beam with an intensity within a given range of intensities in order to generate a beam with a limited frequency distribution. For example, a nanotube can be chosen having a screw axis order and a radius so that when irradiated with a beam of a given frequency with an intensity within a given range of intensities so that only the first harmonic pair has a significant intensity, thus producing a practically dichromatic beam of x-rays. Although technically more difficult, it is clear that even a monochromatic beam of x-rays can be produced in this way.

[0028] Nanotubes are also a preferred material for use in the device of the present invention on a practical level. Being large and easily manipulated molecules nanotubes can be oriented and fixed in space to make a spatially defined solid target

[0029] For example, individual nanotubes may be mounted on a suitable substrate. For example, Hongjie Dai et al., “Nanotubes as nanoprobes in scanning probe microscopy”, Nature, Vol. 384 pp. 147-150 (14 Nov. 1996), which is incorporated by reference for all purposes as if fully set forth herein, discloses the attachment of nanotubes to a silicon substrate using an acrylic adhesive.

[0030] Many nanotubes have been mounted parallel to each other and perpendicular to a polymer substrate, as shown by de Heer et al., “Aligned carbon nanotubes films: production and optical and electronic properties”, Science, Vol. 268 pp. 845-847 (12May 1995), which is incorporated by reference for all purposes as if fully set forth herein.

[0031] Arrays of nanotubes have been assembled as shown by Fan et al, “Self-Oriented Regular Arrays of Carbon Nanotubes and Their Field Emission Properties”, Science, Vol. 283 pp. 512-514 (22 Jan. 1999), which is incorporated by reference for all purposes as if filly set forth herein.

[0032] Bundles of parallel nanotubes have been assembled as shown by Thess et al., “Crystaffine Ropes of Metallic Carbon Nanotubes”, Science, Vol. 273 pp. 483-487 (26 Jul. 1996), Wildoer et al., “Electronic structure of atomically resolved carbon nanotubes”, Nature, Vol. 391 pp. 59-62 (1 Jan. 1998), Liu et al., “Synthesis of Macroscopically Long Ropes of Well-Aligned Single-Walled Carbon Nanotubes”, Advanced Materials, Vol. 12, pp. 1190-1192 (August 2000) and by Lopéz et al., “Novel Polygonized Single-Wall Carbon Nanotube Bundles”, Phys. Rev. Lett., Vol. 86 pp. 3056-3059 (2 Apr. 2001), which are all incorporated by reference for all purposes as if fully set forth herein.

[0033] In Lopez et al certain relatively large-diameter carbon nanotubes are reported to have the tendency to deform to have a hexagonal cross section when found within a bundle. Thus, in cases where it is desired to use a specific nanotube according to the present invention, and the specific nanotube is of type that is found to undergo such a deformation, it is preferred to use discrete nanotubes imbedded in or attached to a substrate such as a polymer rather than use a bundle of the specific nanotubes.

[0034] Launois et al., in “Carbon Nanotubes Synthesized in Chapels of AlPO₄-5 Single Crystals: First X-Ray Scattering Investigations” Solid State Comm. Vol. 116, pp. 99-103 (2000), disclose the production of nanotubes in a single zeolite crystal.

[0035] As is known to one skilled in the art, nanotubes suitable for use in manufacture of a device of the present invention are available from a plurality of manufacturers, for example Material and Electrical Research Corporation of Tucson Ariz.

[0036]FIG. 2 is a schematic illustration, partly in perspective, of a device 10 of the present invention. A plurality of (12.6)-nanotubes 12 are imbedded in and held in place by a polymer substrate 14. Nanotubes 12 are all oriented so that their screw axes 16 are parallel. Flowing around nanotubes 12 and through channel 18 in polymer substrate 14 is liquid helium to reduce thermal twisting and thermal bending of nanotubes 12. A laser device 20 directs a beam 22 of coherent, circularly polarized light towards nanotube assembly so that beam 22 is parallel to the screw axes 16 of nanotubes 12. Suitable laser devices 20 are described in the review article by L'Huiller, et al., referenced hereinabove. Methods to transform linearly polarized coherent light into circularly polarized coherent light, using beam splitters and quarter wave plates are well known in the art. Suitable quarter wave plates are available inter alia from Spindler & floyer GMBH & Co., Göttingen, Germany.

[0037] The interaction of beam 22 with nanotubes 12 produces higher harmonics of beam 22. Because of the very high order of screw axes 16 of nanotubes 12, the produced higher harmonics are very restricted in frequency content. Higher harmonics in the soft x-ray band emerge from the end of the nanotubes 12 opposite to laser device 20.

[0038] In another embodiment of the device of the present invention, 24, depicted in FIG. 3, a beam 22′ of elliptically polarized light is projected towards nanotubes 12′, at an angle α to normal incidence. Beam 22′ is such that the effective electrical field thereof in a plane perpendicular to the nanotube axes is circularly polarized. Such oblique incidence is useful in case light reflected back to laser device 20′ might damage laser device 20′. Although, strictly speaking, tilting beam 22′ prevents beam 22′ from propagating in parallel to screw axes 16′ so that the selection rules described hereinabove are no longer exact, at a sufficiently small angle α the propagation of beam 22′ is close enough to exact for practical purposes and substantially selective generation of high harmonics of beam 22′.

[0039] WO 99/33084 discloses a device and a method based on dipole approximations with respect to both the incident and emitted radiation. The device and the method of the present invention are based on the general and exact method for formulating the selection rules for high harmonic generation beyond that of the dipole approximations, described in the Appendix and Alon et al.. Although superficially resembling the device and the method disclosed in WO 99/33084, the device and the method of the present invention are neither obvious from nor anticipated by WO 99/33084 and specifically, from the theoretical considerations presented therein.

[0040] While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made. 

What is claimed is:
 1. A device for producing high frequency radiation, comprising: (a) a source of elliptically polarized radiation; and (b) a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2, wherein said at least one constituent is oriented so that said elliptically polarized radiation propagates substantially parallel to said screw axis.
 2. The device of claim 1 wherein said source includes a laser.
 3. The device of claim 1 wherein said elliptically polarized radiation includes an electrical field that is circularly polarized in a plane substantially perpendicular to said screw axis.
 4. The device of claim 1 wherein said radiation is circularly polarized.
 5. The device of claim 1 wherein said at least one constituent is a nanotube.
 6. The device of claim 5 wherein said nanotube is single walled.
 7. The device of claim 1 wherein said at least one constituent is a bundle of nanotubes.
 8. The device of claim 1, wherein said medium includes a plurality of said constituents.
 9. The device of claim 1 further comprising; (c) a mechanism for cooling said at least one constituent.
 10. The device of claim 9, wherein said mechanism includes a cryogenic liquid.
 11. The device of claim 1 further comprising: (c) a mechanism for maintaining said orientation of said at least one constituent.
 12. The device of claim 1, wherein said at least one constituent is at least two constituents, and further comprising: (c) a mechanism for maintaining said at least two constituents in a common said orientation.
 13. The device of claim 12, wherein said at least two constituents include nanotubes and wherein said mechanism includes a substrate to which said constituents are attached.
 14. The device of claim 13 wherein said substrate is substantially planar.
 15. The device of claim 13 wherein said substrate includes a polymer material.
 16. The device of claim 13 wherein said substrate includes a crystalline material.
 17. The device of claim 16 wherein said crystalline material is a zeolite.
 18. The device of claim 13 wherein said attachment includes the use of an adhesive.
 19. A method of producing high frequency radiation, comprising: (a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2; and (b) directing elliptically polarized radiation at an angle to said axis such that said elliptically polarized radiation propagates substantially parallel to said screw axis.
 20. The method of claim 19 wherein said elliptically polarized radiation includes an electrical field that is circularly polarized in a plane substantially perpendicular to said screw axis.
 21. The method of claim 19, wherein said at least one constituent is a nanotube.
 22. The method of claim 21 wherein said nanotube is single walled.
 23. The method of claim 19, further comprising: (c) cooling said at least one constituent.
 24. The method of claim 19, wherein said medium includes a plurality of said constituents, the method further comprising the step of: (c) imposing a common orientation on said constituents.
 25. The method of claim 19, wherein said elliptically polarized electromagnetic radiation is circularly polarized.
 26. A device for producing high frequency radiation, comprising: (a) a source of elliptically polarized radiation; and (b) a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2 and also including an axis of approximate C_(n) symmetry, wherein n is at least 3, wherein said at least one constituent is oriented so that said elliptically polarized radiation propagates substantially parallel to said screw axis.
 27. The device of claim 26 wherein said source includes a laser.
 28. The device of claim 26 wherein said elliptically polarized radiation includes an electrical field that is circularly polarized in a plane substantially perpendicular to said screw axis.
 29. The device of claim 26 wherein said radiation is circularly polarized.
 30. The device of claim 26 wherein said at least one constituent is a nanotube.
 31. The device of claim 30 wherein said nanotube is single walled.
 32. The device of claim 26 wherein said at least one constituent is a bundle of nanotubes.
 33. The device of claim 26, wherein said medium includes a plurality of said constituents.
 34. The device of claim 26 further comprising; (c) a mechanism for cooling said at least one constituent.
 35. The device of claim 34, wherein said mechanism includes a cryogenic liquid.
 36. The device of claim 26 farther comprising: (c) a mechanism for maintaining said orientation of said at least one constituent.
 37. The device of claim 26, wherein said at least one constituent is at least two constituents, and farther comprising: (c) a mechanism for maintaining said at least two constituents in a common said orientation.
 38. The device of claim 37, herein said at least two constituents include nanotubes and wherein said mechanism includes a substrate to which said constituents are attached.
 39. The device of claim 38 wherein said substrate is substantially planar.
 40. The device of claim 38 wherein said substrate includes a polymer material.
 41. The device of claim 38 wherein said substrate includes a crystalline material.
 42. The device of claim 41 wherein said crystalline material is a zeolite.
 43. The device of claim 38 wherein said attachment includes the use of an adhesive.
 44. A method of producing high frequency radiation, comprising: (a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2 and also including an axis of approximate C_(n) symmetry, wherein n is at least 3; and (b) directing elliptically polarized radiation at an angle to said axis such that said elliptically polarized radiation propagates substantially parallel to said screw axis.
 45. The method of claim 44 wherein said elliptically polarized radiation includes an electrical field that is circularly polarized in a plane substantially perpendicular to said screw axis.
 46. The method of claim 44, wherein said at least one constituent is a nanotube.
 47. The device of claim 46 wherein said nanotube is single walled.
 48. The method of claim 44, further comprising: (c)cooling said at least one constituent.
 49. The method of claim 44, wherein said medium includes a plurality of said constituents, the method further comprising the step of: (c) imposing a common orientation on said constituents.
 50. The method of claim 44, wherein said elliptically polarized electromagnetic radiation is circularly polarized.
 51. A method of producing a beam of high frequency radiation composed of a limited number of wavelengths, comprising: a) providing a frequency multiplication medium including at least one constituent having approximate finite symmetry including a screw axis of approximate Nth order symmetry, wherein N is at least 2; and b) directing elliptically polarized radiation at an angle to said axis such that said elliptically polarized radiation propagates substantially parallel to said screw axis, said radiation having an intensity sufficiently low to produce only the radiation of the limited number of wavelengths.
 52. The method of claim 51 wherein radiation emitted by a radiation source is attenuated to achieve said intensity of said elliptically polarized radiation.
 53. The method of claim 51 wherein said radiation source is a laser.
 54. The method of claim 51 wherein said constituent is a nanotube.
 55. The method of claim 54 wherein said nanotube is single walled.
 56. The method of claim 51 wherein said elliptically polarized radiation includes an electrical field that is circularly polarized in a plane substantially perpendicular to said screw axis.
 57. The method of claim 51, wherein said elliptically polarized electromagnetic radiation is circularly polarized.
 58. The method of claim 51, wherein said medium includes a plurality of said constituents, the method further comprising the step: (c) imposing a common orientation on said constituents. 